### The Eta Pairing Revisited

F. Hess, N. P. Smart, and F. Vercauteren

##### Abstract

In this paper we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Baretto et al., to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of curves which have large security parameters, complex multiplication by $D=-3$, and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves.

Note: Minor corrections and extra explanation included

Available format(s)
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
nigel @ cs bris ac uk
History
2006-06-16: last of 5 revisions
See all versions
Short URL
https://ia.cr/2006/110

CC BY

BibTeX

@misc{cryptoeprint:2006/110,
author = {F.  Hess and N. P.  Smart and F.  Vercauteren},
title = {The Eta Pairing Revisited},
howpublished = {Cryptology ePrint Archive, Paper 2006/110},
year = {2006},
note = {\url{https://eprint.iacr.org/2006/110}},
url = {https://eprint.iacr.org/2006/110}
}

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